Asymptotics of Sobolev orthogonal polynomials for coherent pairs of Laguerre type

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:245

Article

Meijer, HG ; Pérez, TE ; Piñar, MA

关键词: Laguerre polynomials;    Sobolev orthogonal polynomials;    coherent pairs;    asymptotic properties;   

DOI  :  10.1006/jmaa.2000.6779

来源: Elsevier

【 摘 要 】

Let {S-n}(n) denote a sequence of polynomials orthogonal with respect to the Sobolev inner product (f, g)(s) = integral f(x)g(x)d psi(0)(x) + lambda integral f'(x)g'(x)d psi(1)(x), where lambda > 0 and {d psi(0), d psi(1)} is a so-called coherent pair with at least one of the measures d psi(0) or d psi(1) a Laguerre measure. We investigate the asymptotic behaviour of S-n(x) outside the supports of d psi(0) and d psi(1), and n --> +infinity. (C) 2000 Academic Press.

【 授权许可】

Free